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Search: id:A001160
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| A001160 |
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sigma_5(n), the sum of the 5th powers of the divisors of n.
(Formerly M5240 N2279)
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+0
96
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| 1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182, 4101152, 5314716, 6436344, 8253300, 9768751, 12252702, 14408200, 17766056, 20511150
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, December 1972, p. 827.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, December 1972, p. 827.
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FORMULA
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Multiplicative with a(p^e) = (p^(5e+5)-1)/(p^5-1). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
G.f. sum(k>=1, k^5*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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CROSSREFS
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Cf. A000005, A000203, A001157-A001159.
Sequence in context: A088703 A034679 A017673 this_sequence A061223 A119782 A008515
Adjacent sequences: A001157 A001158 A001159 this_sequence A001161 A001162 A001163
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KEYWORD
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nonn,easy,mult
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AUTHOR
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njas
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